Assistant Professor of Mathematics
Diplom (M.A.) in Physics, University of Bonn
Vordiplom (B.A.) in Mathematics, University of Bonn
Vordiplom (B.A.) in Physics, University of Bonn
Areas of Expertise
- Algebraic Geometry
- Gauge Theory
- String Theory
Visiting Scholar, University of California Berkeley, Fall 2013.
Scholar of the Kavli Institute for Theoretical Physics (KITP), 2011-2013.
- SU(2)-Donaldson invariants of the complex projective plane, (with Michael Griffin, Ken Ono),
Forum Math. DOI: 10.1515/forum-2013-6013, July 2013.
- M24 Moonshine and Donaldson invariants of CP^2, (with Ken Ono),
Commun. Number Theory Phys. 6 (2013), no. 4, 1-12.
- SO(3)-Donaldson invariants of CP^2 and Mock Theta Functions, (with Ken Ono),
Geom. Topol. 16 (2012), no. 3, 1767-1833.
- Kummer surfaces associated with Seiberg-Witten curves, J. Geom. Phys. 62 (2012), no. 1, 107-123.
- The signature of the Seiberg-Witten surface,
Surveys in differential geometry. Volume XV. Perspectives in mathematics and physics, 255-277, Surv. Differ. Geom., 15, Int. Press, Somerville, MA, 2011.
- Donaldson invariants of CP^1 x CP^1,
Commun. Number Theory Phys. 5 (2011), no. 1, 203-229.
- The eigenvalue equation on the Eguchi-Hanson space, J. Math. Phys. 44 (2003), no. 9, 4308-4343.
- Relativitaetstheorie auf dem Homecomputer (German). [Visualizing special theory of relativity], Physik in der Schule, 35 (1997), no. 1, 30-33.
Supervised Student Research
Alex Barron, Honors Project (2013), Title: The Eichler-Selberg trace formula for Hecke operators.
Anika Lindemann, Honors Project (2012), Title: Parity of rank in a rational elliptic surface.
Irina Cazan, Honors Project (2011), Title: Kalman Filters.
Eli Dupree, Independent Study, Title: Geometric models for computer simulations.
Arjumand Masood, Independent Study, Title: Solitons and the geometry of the KdV equation.
Christopher Hoder, Independent Study, Title: PDEs and their applications in quantum mechanics.
Katherine Smith, Independent Study, Title: Integration on manifolds.
Research Talks (Videos)
- Multi-parameter families of K3 surfaces and hypergeometric functions,
Workshop on Hodge Theory in String Theory, November 2013, Fields Institute, Toronto.
- Heterotic/F-theory duality and lattice polarized K3 surfaces,
Workshop on Modular Forms around String Theory, September 2013, Fields Institute, Toronto.
- String-Math, University of Alberta, Edmonton, June 9-13, 2014.
- AMS Special Session on Arithmetic of Algebraic Curves, University of Tennessee, Knoxville, March 21-23, 2014.
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